A method for star point extraction based on attitude information

Abstract

A star point extraction method based on attitude information according to the present invention includes five major steps: constructing a vertical coordinate matrix M, constructing a difference matrix Q, removing noise points and extracting seed points, accurately extracting internal pixels of star points and centroid positioning, and outputting a recursive star point centroid position based on the attitude change amount of inertial devices. Compared with the prior art, the adaptive threshold is determined by the real-time image, which reduces the calculation amount to the greatest extent and improves the real-time performance; when constructing the vertical coordinate matrix, the adopted row step size reduces the general calculation amount; the difference matrix is constructed based on the vertical coordinate matrix, which is reflected in that the discrete sequence has very high discrimination, can accurately remove noise points and extract the desired seed points. Under the combined action of the vertical coordinate matrix and the difference matrix, the accuracy and real-time performance level of star point extraction can be ensured simultaneously; the recursive star point centroid position is output by using the attitude change amount of inertial devices, which solves the problem of fast star point extraction in the normal navigation state and has a wider scope of application.

Description

Technical Field

[0001] The present invention belongs to the technical field of astronomical positioning and orientation, and relates to a star point extraction method based on attitude information. Background Technique

[0002] The main task of star point extraction is to obtain the two-dimensional coordinate information of the stars in the field of view of the star sensor on the CCD plane through a series of processes. In order to make the final two-dimensional coordinate information as accurate as possible, when designing the star sensor, defocusing processing is used to project the stars into a dot-like diffuse area, and the energy distribution model of this area usually conforms to the Gaussian distribution. Therefore, the star point extraction process is actually the application of the positioning technology of point-like targets in the star map processing of star sensors. Star point extraction is an important part of the entire task plan of the star sensor and is also the first task to be processed after the star map is output. Star point extraction mainly involves two technical indicators: one is the star point extraction speed, and the other is the star point extraction accuracy. The star point extraction speed affects the overall real-time level of the star sensor, and the star point extraction accuracy affects the success rate of the next star identification and the final attitude determination accuracy of the star sensor. Generally speaking, star point extraction includes two major steps: precise extraction of the star point pixel area and centroid positioning. The precise extraction of the star point pixel area can be further divided into the following two steps. One is to distinguish the background noise of the image from the target area (star point diffuse area); the other is to aggregate and classify the target area to obtain the precise distribution of the star points. The main feature relied on to distinguish the background noise of the image from the star point target area is the gray value. When distinguishing the star point target area from the background noise, the most common method is the threshold segmentation method, which is widely used in the field of image processing and is a typical image segmentation method based on gray features. How many stars in the field of view can be projected onto the CCD plane mainly depends on parameters such as the limit detection magnitude of the star sensor and the field of view size. The higher the limit detection magnitude and the larger the field of view, the more stars will be imaged on the CCD, which can be up to dozens. Therefore, after distinguishing the star point target area from the background noise, it is necessary to classify and aggregate according to the star points to which the star point pixels belong to obtain the precise distribution of the diffuse areas of each star point itself. At this time, the position relationship of the pixels on the imaging plane of the star sensor becomes the main basis for classifying and aggregating the star point pixels. After finding the precise distribution of different star points in the star map, it is necessary to use the position information and corresponding gray information of the extracted star point diffuse area to solve the two-dimensional centroid coordinates of the star point. The sub-pixel interpolation positioning algorithm can achieve centroid positioning accuracy at the sub-pixel level and is currently the most widely used star point subdivision positioning algorithm. Wang Zhaokui et al. published an article titled "A Fast Algorithm for Star Point Positioning in CCD Star Maps" in the 26th volume, issue 3 of Acta Scientiarum Naturalium Universitatis Pekinensis in 2006. By performing two gray projections, the distribution of the star point area can be obtained quickly. This method greatly reduces the computational amount and storage amount and has certain practical engineering application value. However, if there are overlapping star points (horizontal or vertical axis) on the star map, the star point area obtained by this method will be wrongly enlarged; in addition, the star point area obtained by this method can only be rectangular in shape, and it is difficult to depict the accurate edge of the star point area. Therefore, although this method is efficient, it is difficult to accurately determine the range of the star point area.The article "Star image extraction based on local region growth of block peak points" published by Wang Haiyong et al. in the 11th issue of Volume 20 of "Optics and Precision Engineering" in 2012 proposed a method of using block peak points as "seed" points to determine the star point region based on local region growth. This method determines the number of star map blocks according to the minimum angular distance requirement of star map recognition, takes the pixel with the largest gray value in each block as the "seed" point, and performs local region growth to obtain the star point region. The article "Accuracy analysis of centroid calculated by a modified center detection algorithm for Shack–Hartmann wavefront sensor" published by Li et al. in the 281st issue of "Optics Communications" in 2008 analyzed the accuracy performance of the centroid method with different powers of pixel signals as weights under different signal-to-noise ratio conditions. The research results show that this method has high accuracy under additive noise conditions, but is easily affected by noise related to starlight signals such as photon shot noise. The invention patent application "A method for extracting star point centroid based on attitude association" proposed by Zhou Zhaofa et al. in 2021 has the same invention purpose as the present invention, but uses the gray cross-projection method based on distance discrimination and a new target area marking method to extract star points in the star map. The methods involved are irrelevant and independent in terms of the technologies adopted, and have completely different core theories. The above-mentioned literature's research on the systematic error of the star point subdivision positioning algorithm is mostly based on numerical simulation and simulation, and the obtained results are empirical. The article "A Novel Two-Scan Connected-Component Labeling Algorithm" published by He et al. in the 229th issue of "Lecture Notes in Electrical Engineering" in 2013 derived the relationship between the systematic error and the Gaussian radius of the star point under the condition of a finite sampling window based on a simplified Gaussian distribution model of star point energy. This method can explain the optimal star point size, but it ignores the pixel response function and the influence of different pixel positions. To sum up, although many scholars have given corresponding solutions in the field of star point extraction, how to achieve a better balance between the real-time level of star point extraction and the accuracy of star point extraction is still an urgent problem to be solved at present, and it is necessary to further improve the performance of star point extraction of star sensors based on the existing knowledge theory. Summary of the Invention

[0003] To solve the problems existing in the prior art, the present invention proposes a star point extraction method based on attitude information, which solves the compatibility problem between the real-time performance and accuracy of star point extraction. On the basis of ensuring good measurement accuracy and real-time performance, it has a wider scope of application.

[0004] Now, the concept and technical solution of the present invention will be described as follows:

[0005] The basic idea of the present invention is to randomly select several sampling windows according to the actually taken star map. The distribution of the sampling windows should be as uniform as possible, and the size of the sampling windows should be appropriate to reflect the noise characteristics. Calculate the expectation and standard deviation of the gray values of all pixels in each sampling window, and then calculate the threshold for star map noise reduction processing; determine the size of the ordinate matrix M according to the noise intensity of the star map. Scan the entire star map with a row step size of 2 to obtain the ordinate matrix M. Each row of the ordinate matrix M stores the ordinates of the potential pixels selected from the corresponding row of the star map. The selected potential pixel points are the set of noise points (strong noise points with gray values greater than the threshold) and the seed points of different star points; perform a first-order forward difference on each row of the ordinate matrix M to obtain the difference matrix Q. If the position (2i - 1, M(i, j)) of the star map S pointed to by a certain value M(i, j) in the ordinate matrix M is a seed point (i.e., the pixel is in the inner region of the star point), then for a certain row of pixel points (usually with a length of 1 - 7) in the inner region of the same star point, its corresponding position in the ordinate matrix M shows a linear increase, and the result of performing a first-order forward difference on it is a constant sequence {1}. This property plays an important role in accurately extracting seed points; traverse each row of the difference matrix Q, and extract seed points by judging whether there are 2 or more consecutive 1 values in each row of the difference matrix Q, and eliminate the same kind of seed points based on the Manhattan distance. According to the coordinate information of the seed points, use the region growing method to search for all the inner pixels of the star point and perform centroid positioning. The growth criterion of region growing is that the absolute value of the difference between the gray value of the growth point and the adjacent pixel points in the 8-neighborhood is less than a certain parameter k, and the value of the parameter k depends on the experimental situation. Output the seed points of the star points in the subsequent captured star map recursively according to the attitude change amount of the inertial device, and perform region growing and centroid positioning operations, which greatly improves the real-time performance level of the star sensor.

[0006] The technical solution of the present invention is: a star point extraction method based on attitude information, which is characterized in that it includes five major steps: constructing the ordinate matrix M, constructing the difference matrix Q, eliminating noise points and extracting seed points, accurately extracting the inner pixels of the star point and centroid positioning, and outputting the recursive centroid position of the star point based on the attitude change amount of the inertial device. Specifically, it includes:

[0007] Step 1: Traverse the star map S once to obtain the two-dimensional ordinate matrix M;

[0008] Step 2: Perform first-order forward difference on each row of the ordinate matrix M to obtain the difference matrix Q;

[0009] Step 3: Eliminate noise points and extract seed points;

[0010] Step 4: Based on the coordinate information of the seed points, use the region growing method to search for all internal pixels of the star points and perform centroid positioning;

[0011] Step 5: Use the attitude change amount of the inertial device to output the centroid positions of the star points in the subsequent captured star maps recursively.

[0012] The present invention further provides a star point extraction method based on attitude information, characterized in that the specific steps of "performing a single traversal of the star map S to obtain the two-dimensional ordinate matrix M" in Step 1 are as follows:

[0013] Step 1.1: Determine the threshold T. The method is as follows: Randomly select dozens of sampling windows. The distribution of the sampling windows should be as uniform as possible. The size of the sampling windows is appropriate, not too large, as long as it can reflect the noise characteristics. Calculate the expectation μ of the gray values of all pixels within each sampling window i and the standard deviation σ i , and then calculate the threshold T for star map noise reduction processing according to the following formula.

[0014]

[0015] In the formula, μ i is the expectation of the gray values of all pixels within the sampling window, σ i is the standard deviation of the gray values of all pixels within the sampling window, N w is the number of sampling windows, and a is an empirical value, which depends on the test results.

[0016] Step 1.2: For a captured star map S, assume the size of the star map is N1*N2. Here, N1 is the number of rows of the star map, and N2 is the number of columns of the star map. Construct a vertical coordinate matrix M, where the size of M is (N1 / 2)*N3. It is called the vertical coordinate matrix because the non-zero values stored in the matrix are the vertical coordinates of potential pixel points. The number of rows of the M matrix is half of the number of rows of the S matrix, and N3 is a constant value determined according to the noise intensity of the star map. The greater the noise intensity, the more noise pixel points with high gray values (hereinafter referred to as noise points) in the image. When searching for seed points (any pixel point inside a star point is called a seed point of that star point) later, there will be more potential pixel points, and N3 will be larger. Each row of the vertical coordinate matrix M stores the vertical coordinates of the potential pixels selected from the corresponding row of the star map. The selected potential pixel points are the set of noise points (strong noise points with gray values greater than the threshold T) and the seed points of different star points. Subsequently, the vertical coordinate matrix M will be processed twice to remove the noise points and retain the seed points. After obtaining these seed points, all the internal pixel points of different star points can be further quickly searched for centroid positioning.

[0017] Step 1.3: Construct the vertical coordinate matrix M as described below. First, traverse each pixel point in the first row of the star map from left to right. When encountering the first pixel point with a gray value greater than the threshold T, store the vertical coordinate of this pixel point in the position M(1, 1) of the M matrix. When encountering the second pixel point with a gray value greater than the threshold T, store the vertical coordinate of this pixel point in the position M(1, 2) of the M matrix, and so on, until scanning through the data of the first row of the star map. Then, traverse each pixel point in the third row of the star map from left to right. When encountering the first pixel point with a gray value greater than the threshold T, store the vertical coordinate of this pixel point in the position M(2, 1) of the M matrix, and so on, until scanning through the data of the third row of the star map. According to this pattern, scan the entire star map with a row step size of 2 to obtain the vertical coordinate matrix M.

[0018] The present invention further provides a star point extraction method based on attitude information, characterized in that: the specific steps of "performing a first-order forward difference on each row of the vertical coordinate matrix M to obtain a difference matrix Q" in Step 2 are as follows:

[0019] Step 2.1: Construct the difference matrix Q. The specific execution process is as follows: Subtract the data M(i, j - 1) in the (j - 1)-th column of the i-th row of the vertical coordinate matrix M from the data M(i, j) in the j-th column of the i-th row of the vertical coordinate matrix M to obtain the data Q(i, j) in the j-th column of the i-th row of the difference matrix Q, that is

[0020] Q(i,j) = M(i,j) - M(i,j - 1) (2)

[0021] Step 2.2: Explain the mathematical meaning reflected by the first-order difference operation in removing noise points and extracting seed points in the subsequent steps.

[0022] If the position (2i - 1, M(i, j)) of a certain value M(i, j) in the ordinate matrix M pointing to the star map S is a seed point (i.e., this pixel is in the internal area of the star point), generally, the pixel points (2i - 1, M(i, j) - 1) and (2i - 1, M(i, j) + 1) of the star map S are also in the internal area of the star point, or (2i - 1, M(i, j) - 2), (2i - 1, M(i, j) - 1), (2i - 1, M(i, j)), or (2i - 1, M(i, j)), (2i - 1, M(i, j) + 1), (2i - 1, M(i, j) + 2). Generally speaking, there are three adjacent pixel points inside the star point. Here, taking (2i - 1, M(2i - 1, j) - 1), (2i - 1, M(i, j)), (2i - 1, M(i, j) + 1) as an example, for the ordinate matrix M, these three adjacent pixel points inside the star point in the star map will all be recognized and their ordinates stored in step one. Then, there are three adjacent numbers (M(i, j) - 1, M(i, j), M(i, j) + 1) at a certain position in the i-th row of the matrix M. It can be seen that for a certain row of pixel points (usually with a length of 1 - 7) in the internal area of the same star point, their corresponding positions in the ordinate matrix M increase linearly, which is equivalent to the constant slope in a continuous function. At this time, the result obtained by performing the first-order forward difference on it is a constant sequence {1}.

[0023] If a non-zero value M(i, j) in the ordinate matrix M pointing to the position (2i - 1, M(i, j)) of the star map S is not a seed point (i.e., it is a noise point), generally, the pixel points (2i - 1, M(i, j) - 1) and (2i - 1, M(i, j) + 1) of the star map S are not in the internal area of the star point. That is, the pixel points (2i - 1, M(i, j) - 1) and (2i - 1, M(i, j) + 1) of the star map S are usually considered as noise points with lower gray values in step one, and their ordinates will not be stored in the matrix M. Therefore, generally, regardless of whether the values of M(i, j - 1) and M(i, j + 1) in the ordinate matrix M store the ordinates of strong noise points or seed points, M(i, j - 1), M(i, j), and M(i, j + 1) increase non-linearly, that is, M(i, j) - M(i, j - 1) ≠ 1 and M(i, j + 1) - M(i, j) ≠ 1.

[0024] The present invention further provides a star point extraction method based on attitude information, which is characterized in that: the specific steps of "removing noise points and extracting seed points" in step 3 are as follows:

[0025] Step 3.1: Extract the set of seed points. Traverse each row of the difference matrix Q, and extract the seed points by determining whether there are 2 or more consecutive 1 values in each row of the difference matrix Q, that is, if the following conditions are met:

[0026] Q(i,j) = 1 && Q(i,j + 1) = 1 (3)

[0027] Then:

[0028] (2i - 1, M(i,j)) ∈ {Star} (4)

[0029] Where, {Star} is the set of internal pixel points of a certain star point. (2i - 1, M(i,j)) are the horizontal and vertical coordinates of the seed point.

[0030] Step 3.2: Eliminate the similar seed points in the set of seed points. So far, the set of seed points {(2i - 1, M(i,j))} of all star points in the star map has been obtained. As can be seen from Step 1, the row step size when traversing the star map is 2. Although the row step size is 2, redundant seed points will also be generated, that is, some seed points in the set of seed points {(2i - 1, M(i,j))} belong to the same star point and need to be eliminated. For this reason, the similar seed points are eliminated based on the Manhattan distance. For example, for the seed points (x 1 , y 1 ), (x 2 , y 2 ), generally, when the Manhattan distance between the two is less than or equal to 5, it is considered that these two seed points are similar seed points, and any one of them can be eliminated at will, as follows:

[0031] d = |x 1 - x 2 | + |y 1 - y 2 | ≤ 5 (5)

[0032] Where, d is the Manhattan distance between two seed points (x 1 , y 1 ), (x 2 , y 2 ).

[0033] The present invention further provides a star point extraction method based on attitude information, which is characterized in that the specific steps of "searching for all internal pixels of the star point by using the region growing method based on the coordinate information of the seed point and performing centroid positioning" in Step 4 are as follows:

[0034] Step 4.1: Using the seed point as the initial growth point, the growth criterion for region growing is that the absolute value of the difference between the gray value of the growth point and that of its adjacent pixels in the 8-neighborhood is less than a certain parameter k, where k is generally taken as 10 - 30, depending on the experimental situation. The core step of region growing is to start from the initial growth point, merge the pixels with similar features in the 8-neighborhood pixels of this growth point, regard the newly merged pixels as new growth points, and then execute the same steps as above based on these new growth points until there are no new growth points. Therefore, appropriate initial growth points and growth criteria are crucial. The initial growth points have been obtained through Steps 1, 2, and 3, and the growth criterion is as described above. Finally, all the internal pixels of each star point are obtained.

[0035] Step 4.2: With all the internal pixels of the star point, the centroid coordinates of the star point can be obtained according to the centroid positioning formula as follows:

[0036]

[0037] In the formula, x c is the abscissa of the centroid of the star point, y c is the ordinate of the centroid of the star point, x i is the abscissa of the i-th pixel inside the star point, y i is the ordinate of the i-th pixel inside the star point, and g i is the gray value of the i-th pixel inside the star point.

[0038] The present invention further provides a star point extraction method based on attitude information, characterized in that the specific steps of "using the attitude change amount of the inertial device to output and recursively calculate the centroid position of the star points in the subsequent captured star map" in Step 5 are as follows:

[0039] Step 5.1: Determine the three-dimensional coordinates r of the star vector in the star sensor system at the current time t. After obtaining the centroid coordinates of the star vector on the CCD plane at the current time through the above steps, for the subsequent captured star map, the seed points of the star points can be quickly obtained by using the attitude change amount of the inertial device to output, and region growing and centroid positioning operations are performed, greatly improving the real-time level of the star sensor. The specific process is as follows.

[0040] The three-dimensional coordinates r of the star vector in the star sensor system at the current time t can be obtained as follows:

[0041]

[0042] In the formula, are the abscissa and ordinate of the centroid of the star point at time t, x 0 , y 0 are the principal point coordinates of the star sensor, and f is the focal length of the star sensor.

[0043] Step 5.2: Derive the recurrence model between the centroid coordinates of the same star on the CCD plane at time t and time t+Δt. The three-dimensional coordinates of the star vector in the star sensor system at time t+Δt are r t+Δt , r t+Δt and r t are related as follows:

[0044]

[0045] In the formula, is the coordinate system transformation matrix from the star sensor system at time t+Δt to the star sensor system at time t.

[0046] The coordinate system transformation matrix can be obtained from the output of the attitude change of the inertial device as follows:

[0047]

[0048] In the formula, ω t is the angular velocity vector at time t, ω t = [ω x ω y ω z T , is the skew-symmetric matrix of the vector ω t , is the angular increment of the three axes of the gyroscope, which is a known quantity, that is, the coordinate system transformation matrix is known.

[0049] Based on equations (8) and (9), the recurrence relationship between and can be derived as follows:

[0050]

[0051] In the formula, are the horizontal and vertical coordinates of the centroid of the star point at time t+Δt, and the other variables have been explained before.

[0052] Usually, is very small and can be ignored, so the above formula can be simplified to:

[0053]

[0054] So far, the predicted value of the centroid coordinates of the star point can be obtained from the output of the attitude change of the inertial device through equation (10), and then this predicted value can be used as the seed point for region growing and centroid positioning, which greatly improves the processing speed of the star sensor.

[0055] ​The advantages of the present invention compared with the prior art are as follows: the adaptive threshold is determined by the real-time image, which can reduce the calculation amount to the greatest extent and improve the real-time performance on the basis of ensuring the rationality of threshold selection; the ordinate matrix M is constructed with a row step size of 2, reducing the general calculation amount; further, a difference matrix Q is constructed based on the ordinate matrix M. The pixels in the internal area of the star point are reflected as a discrete sequence 1 in the difference matrix Q, which has very high identifiability and can accurately eliminate noise points and extract the desired seed points. Under the combined action of the ordinate matrix M and the difference matrix Q, the accuracy and real-time level of star point extraction can be ensured simultaneously; the recursive star point centroid position is output by using the attitude change amount of the inertial device, solving the problem of fast star point extraction under normal navigation conditions. The method has a wider applicable range on the basis of ensuring good measurement accuracy and real-time performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 : Schematic diagram of starlight vector imaging

[0057] Figure 2 : Simplified schematic diagram of image S

[0058] Figure 3 : Schematic diagram of ordinate matrix M

[0059] Figure 4 : Schematic diagram of difference matrix Q

[0060] Figure 5 : Row coordinate error

[0061] Figure 6 : Column coordinate error DETAILED DESCRIPTION OF THE INVENTION

[0062] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0063] The present invention proposes a star point extraction method based on attitude information, including five major steps: constructing an ordinate matrix M, constructing a difference matrix Q, eliminating noise points and extracting seed points, accurately extracting internal pixels of the star point and centroid positioning, and outputting a recursive star point centroid position based on the attitude change amount of the inertial device.

[0064] The overall workflow is as follows: First, randomly select several appropriately sized sampling windows in the actual captured star map, calculate the expectation and standard deviation of the gray values of all pixels within each sampling window, and then calculate the threshold value. Then, estimate the noise intensity of the star map to determine the size of the ordinate matrix M. Scan the entire star map with a row step size of 2 to obtain the ordinate matrix M. Each row of the ordinate matrix M stores the ordinates of the potential pixels selected from the corresponding row of the star map. Next, perform a first-order forward difference on each row of the ordinate matrix M to obtain the difference matrix Q. Furthermore, traverse each row of the difference matrix Q, extract the seed points by determining whether there are two or more consecutive 1 values in each row of the difference matrix Q, and eliminate the same type of seed points based on the Manhattan distance. Finally, according to the coordinate information of the seed points, use the region growing method to search for all internal pixels of the star points and perform centroid localization. The growth criterion for region growing is that the absolute value of the difference between the gray value of the growth point and the gray values of the 8-neighborhood adjacent pixels is less than a certain parameter k, and the value of the parameter k depends on the experimental situation. In addition, for subsequent captured star maps, output the seed points of the recursive star points according to the attitude change amount of the inertial device, and perform region growing and centroid localization operations to ensure the real-time level of the star sensor in the normal navigation state.

[0065] Embodiment:

[0066] See Figure 1 :

[0067] For the convenience of explanation, take Figure 2 as an example for a brief explanation. Figure 1 is a simplified schematic diagram of stellar imaging. The three-dimensional coordinates r of the stellar vector in the star sensor system at time t are:

[0068]

[0069] In the formula, are the horizontal and vertical coordinates of the centroid of the star point at time t, x 0 , y 0 are the coordinates of the principal point of the star sensor, and f is the focal length of the star sensor.

[0070] Step 1: Traverse the star map image S once to obtain the two-dimensional ordinate matrix M.

[0071] See Figure 2 , Figure 3 :

[0072] Step 1.1: Determine the threshold T. Before constructing the ordinate matrix M, it is necessary to first determine the size of the threshold parameter T. Randomly select two sampling windows in the image S. The distribution of the sampling windows should be as uniform as possible. The size of the sampling window is 2*2. Calculate the expectations μ 1 , μ 2 and the standard deviations σ of the gray values of all pixels within these two sampling windows1 , σ 2 , and then calculate the threshold value T according to the following formula:

[0073]

[0074] In the formula, the number of sampling windows N w is taken as 2, the parameter a is taken as 1, and it is assumed that the calculated threshold value T is 4.

[0075] Step 1.2: Construct the ordinate matrix M. For the star map image S, the image size is 12 * 12, that is, the number of rows of the star map is 12 and the number of columns is also 12. Initialize an ordinate matrix M, where the size of M is 6 * 7, the parameter N3 is set to 7, and the initial values in the matrix are all set to 0. The non-zero values stored in the ordinate matrix are the ordinates of potential pixel points. Each row of the ordinate matrix M stores the ordinates of the potential pixels selected in the corresponding row of the star map. The selected potential pixel points are a set of noise points and seed points. Subsequently, a first-order forward difference process will be performed on the ordinate matrix M to eliminate the noise points and retain the seed points. After obtaining these seed points, all the internal pixel points of different star points can be further quickly searched for centroid positioning. The construction method of the ordinate matrix M is described as follows.

[0076] Step 1.3: Construct the ordinate matrix M. First, traverse the first row of pixels of the star map image S from left to right. For the first and second pixels, their grayscale values ​​are less than the threshold value 4, so their ordinates are not recorded in the ordinate matrix M; for the third pixel, its grayscale value is greater than the threshold value 4, so the ordinate 3 of this pixel is stored in the M(1,1) position of the M matrix; for the fourth pixel, its grayscale value is also greater than the threshold value 4, so the ordinate 4 of this pixel is stored in the M(1,2) position of the M matrix; for the fifth to twelfth pixels, their grayscale values ​​are less than the threshold value 4, so their ordinates are not recorded in the ordinate matrix M, and the scanning of the first row of image data is completed. Then, the pixels of the third row of the star map image S are traversed from left to right. For the first pixel, its grayscale value is less than the threshold value 4, so its ordinate is not recorded in the ordinate matrix M; for the second to fifth pixel, its grayscale value is greater than the threshold value 4, so the ordinates 2, 3, 4, 5 of these pixels are stored in the M(2, 1) to M(2, 4) positions of the M matrix in sequence; for the sixth to eighth pixel, its grayscale value is less than the threshold value 4, so its ordinate is not recorded in the ordinate matrix M; for the ninth pixel, its grayscale value is greater than the threshold value 4, so the ordinate 9 of this pixel is stored in the M(2, 5) position of the M matrix. Similarly, the ordinate 11 of the eleventh pixel is stored in the M(2, 6) position of the M matrix. Finally, the third row of data of the image is scanned to obtain the second row of data of the M matrix. Next, we traverse the pixels of the fifth row of the star map image S from left to right. The data of the fifth row contains neither the internal pixels of the star points nor the strong noise points, so the data of the third row of the M matrix remains all zero. According to this pattern, we continue to scan the 7th, 9th, and 11th rows of the star map image S to obtain the final ordinate matrix M, as shown in Figure 3 shown.

[0077] Step 2: Perform a first-order forward difference on each row of the ordinate matrix M to obtain the difference matrix Q.

[0078] See also Figure 4 :

[0079] Step 2.1: Construct the difference matrix Q, and the specific construction process is as follows. First, traverse the data points in the first row of the ordinate matrix M from left to right. For the first data point, there is no data point on its left, so let Q(1, 1) = M(1, 1) = 3; for the second data point, Q(1, 2) is the difference between M(1, 2) and M(1, 1), that is, Q(1, 2) = 1; for the third data point, Q(1, 3) is the difference between M(1, 3) and M(1, 2), that is, Q(1, 3) = -4; for the 4th to 7th data points, it is easy to find that Q(1, 4) to Q(1, 7) = 0. Then, traverse the data points in the second row of the ordinate matrix M from left to right. For the first data point, there is no data point on its left, so let Q(2, 1) = M(2, 1) = 2; for the second data point, Q(2, 2) is the difference between M(2, 2) and M(2, 1), that is, Q(2, 2) = 1; similarly, we can get Q(2, 3) = 1, Q(2, 4) = 1, Q(2, 5) = 4, Q(2, 6) = 2, Q(2, 7) = -11. According to this pattern, continue to scan the data in the 3rd, 4th, 5th, and 6th rows of the ordinate matrix M to obtain the final difference matrix Q, as Figure 4 shown.

[0080] Step 2.2: It can be seen that the position (2 * 2 - 1, M(2, 2)) = (3, 3) of the value M(2, 2) = 3 in the ordinate matrix M pointing to the star map S is the seed point, and the pixel points (3, 2), (3, 4), (3, 5) of the star map image S are also in the internal area of the star point, that is, there are four adjacent pixel points in the data of this row of the star point. For the ordinate matrix M, these four adjacent pixel points of the star point will be recognized and their ordinates will be stored in Step 1, so there are four adjacent numbers (2, 3, 4, 5) in the second row of the matrix M. As mentioned above, for this row of pixel points (with a length of 4) in the internal area of the star point, their corresponding positions in the ordinate matrix M are indeed linearly increasing. At this time, the result of the first-order forward difference of (2, 3, 4, 5) is the constant sequence {1, 1, 1}.

[0081] For the non-zero value M(2, 5) in the vertical coordinate matrix M, the position it points to on the star map S, (2*2 - 1, M(2, 5)) = (3, 9), is not a seed point (i.e., it is a noise point), and the pixel points (3, 8) and (3, 10) of the star map S are not in the inner region of the star point. That is, the pixel points (3, 8) and (3, 10) of the star map S are considered noise points with lower gray values in step one, and their vertical coordinates will not be stored in the matrix M. Moreover, the value M(2, 4) of the vertical coordinate matrix M stores the vertical coordinate of the seed point M(2, 4) = 5, and M(2, 6) stores the vertical coordinate of the strong noise point M(2, 6) = 11. It can be seen that M(2, 4), M(2, 5), and M(2, 6) do not grow linearly, that is, M(2, 5) - M(2, 4) = 4 ≠ 1, M(2, 6) - M(2, 5) = 2 ≠ 1.

[0082] As can be seen from the above, the properties of seed points and non-seed points reflected in the vertical coordinate matrix M are different, which provides a good prerequisite for the subsequent accurate extraction of seed points.

[0083] Step 3: Eliminate noise points and extract seed points.

[0084] See Figure 3 、 Figure 4 :

[0085] Step 3.1: Extract seed points. The specific extraction process is as follows. First, traverse the data of the first row of the difference matrix Q from left to right. For the first data point, if Q(1, 1) ≠ 1, then continue to judge the second data point; since Q(1, 2) = 1, so judge whether Q(1, 3) is equal to 1. If Q(1, 3) = 1, then the data point Q(1, 2) satisfies the seed point constraint condition (Equation (3)): Q(i, j) = 1 && Q(i, j + 1) = 1. At this time, it is considered that the position (2 * 1 - 1, M(1, 2)) = (1, 4) of the star map image S pointed to by M(1, 2) is a seed point. However, here, Q(1, 3) ≠ 1, so the position of the star map image S pointed to by the data point M(1, 2) is not a seed point; continue to judge the third data point. Since Q(1, 3) ≠ 1, the traversal of the data in the first row of the difference matrix Q is completed. Then, traverse the data of the second row of the difference matrix Q from left to right. For the first data point, if Q(2, 1) ≠ 1, then continue to judge the second data point; since Q(2, 2) = 1, so judge whether Q(2, 3) is equal to 1. Q(2, 3) also happens to be equal to 1, so Q(2, 2) satisfies the seed point constraint condition, and the position (3, 3) of the star map image S pointed to by M(2, 2) is stored in the seed point set; continue to judge the third data point. Since Q(2, 3) = 1, so judge whether Q(2, 4) is equal to 1. Q(2, 4) also happens to be equal to 1, so Q(2, 3) also satisfies the seed point constraint condition, and the position (3, 4) of the star map image S pointed to by M(2, 3) is also stored in the seed point set; continue to judge the 4th to 7th data points. Since Q(2, 4) to Q(2, 7) do not satisfy the seed point constraint condition, there is no seed point. According to this pattern, continue to scan the data of the 3rd, 4th, 5th, and 6th rows of the difference matrix Q and extract the seed points among them. Finally, the seed point set can be obtained: {(3, 3), (3, 4), (9, 8), (9, 9)}. Comparing with Figure 2 in the star map image S, it can be verified that the pixel points (3, 3), (3, 4), (9, 8), and (9, 9) of the star map image S do belong to the star point diffusion region, and the seed points are extracted correctly.

[0086] Step 3.2: Elimination of redundant seed points. So far, the set of seed points for all star points in image S has been obtained as {(3, 3), (3, 4), (9, 8), (9, 9)}. It can be found that there are redundant seed points in the set of seed points, that is, some seed points in the set belong to the same star point and need to be eliminated. For this purpose, Manhattan distance is used to eliminate seed points of the same kind. For the seed points (3, 3) and (3, 4), the Manhattan distance d = |3 - 3| + |3 - 4| = 1 < 5, and it is considered that these two seed points belong to the same kind of seed points, and the seed point (3, 3) can be eliminated; similarly, for the seed points (9, 8) and (9, 9), the Manhattan distance d = |9 - 9| + |8 - 9| = 1 < 5, and it is considered that these two seed points belong to the same kind of seed points, and the seed point (9, 8) is eliminated. Finally, the obtained set of seed points is {(3, 4), (9, 9)}. So far, the seed point search work is completed.

[0087] Step 4: Based on the information of the set of seed points {(3, 4), (9, 9)}, use the region growing method to search for all internal pixels of the star points and perform centroid localization.

[0088] See Figure 1 、 Figure 5 、 Figure 6 :

[0089] Step 4.1: Precise extraction of the internal pixel region of the star point. First, taking the seed point (3, 4) as the initial growth point, search for all the internal pixel points of this star point. The growth criterion for region growing is that the absolute value of the difference between the gray value of the growth point and the gray values of its 8-neighborhood adjacent pixels is less than the parameter 4. Starting from the seed point (3, 4), calculate the absolute values of the differences between the gray value of the seed point (3, 4) and the gray values of its 8-neighborhood adjacent pixels {(2, 3), (2, 4), (2, 5), (3, 3), (3, 5), (4, 3), (4, 4), (4, 5)}, which are {0, 0, 0, 0, 0, 0, 0, 7} respectively. Therefore, 7 of the adjacent pixels {h1 = (2, 3), h2 = (2, 4), h3 = (2, 5), h4 = (3, 3), h5 = (3, 5), h6 = (4, 3), h7 = (4, 4)} are all considered as the internal pixel region of the star point and these 7 adjacent pixels are set as the new growth points. Continuing with h1 as the starting point, calculate the absolute values of the differences between the gray value of h1 and the gray values of its 8-neighborhood adjacent pixels, which are {6, 0, 0, 0, 0, 0, 0, 0} respectively. Therefore, 7 of the adjacent pixels are all considered as the internal pixel region of the star point. Among these 7 adjacent pixels, four are newly emerged growth points, namely {h8 = (1, 3), h9 = (1, 4), h10 = (2, 2), h11 = (3, 2)}. These four newly emerged growth points will all perform the same operation as h1 to search for all the internal pixel points of the star point. Grow continuously according to this pattern until all the growth points have finished growing. Finally, all the internal pixel points of this star point are obtained as {(1, 3), (1, 4), (2, 2), (2, 3), (2, 4), (2, 5), (3, 2), (3, 3), (3, 4), (3, 5), (4, 3), (4, 4)}, and the gray values are {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9} in sequence. With the same idea, all the internal pixel points and the corresponding gray values of the star point containing the seed point (9, 9) can be obtained.

[0090] Step 4.2: Star point centroid positioning. With all the internal pixel points of the star point and the corresponding gray values, the centroid coordinates of the above two star points can be obtained respectively according to the centroid positioning formula as follows:

[0091]

[0092] In the formula, x c is the abscissa of the star point centroid, y c is the ordinate of the star point centroid, x i is the abscissa of the i-th pixel point inside the star point, y i is the ordinate of the i-th pixel point inside the star point, g i is the gray value of the i-th pixel point inside the star point.

[0093] Step 5: Output the centroid positions of the star points in the subsequent captured star maps by using the attitude change amount of the inertial device.

[0094] Step 5.1: Determine the three-dimensional coordinates r of the star vector in the star sensor system at the current time t. Given the centroid coordinates of the star vector on the CCD plane at the current time, the three-dimensional coordinates r of a certain star vector in the star sensor system at the current time t are as follows:

[0095]

[0096] In the formula, are the horizontal and vertical coordinates of the centroid of the star point at time t, x 0 , y 0 are the principal point coordinates of the star sensor, and f is the focal length of the star sensor.

[0097] Step 5.2: Deduce the recurrence model between the centroid coordinates of the same star on the CCD plane at time t and time t+Δt. The three-dimensional coordinates of the star vector in the star sensor system at time t+Δt are r t+Δt , r t+Δt and r t are related as follows:

[0098]

[0099] In the formula, is the coordinate system transformation matrix from the star sensor system at time t+Δt to the star sensor system at time t.

[0100] The coordinate system transformation matrix can be obtained from the output of the attitude change amount of the inertial device, as follows:

[0101]

[0102] In the formula, ω t is the angular velocity vector at time t, ω t = [ω x ω y ω z T , is the skew-symmetric matrix of the vector ω t , is the angular increment of the three axes of the gyroscope, which is a known quantity, that is, the coordinate system transformation matrix is known.

[0103] Based on the above two formulas, the recurrence relationship between and can be deduced as follows:

[0104] ​

[0105] So far, the predicted value of the star centroid coordinates can be quickly obtained by using the attitude change amount output of the inertial device through the above formula, and then this predicted value is used as the seed point for region growing and centroid positioning, which greatly improves the processing speed of the star sensor.

[0106] The SKY2000 star catalog is used as the basic star catalog, and the limiting magnitude of the star sensor is set to 6. The resolution of the simulated star map image is set to 512×512 pixels, the field of view of the star sensor is 6°×6°, and the gray level of the simulated star map is 0 - 255. The mean value of the Gaussian white noise is set to 0, and the standard deviation is set to 6 to obtain the corresponding simulated star map, and the star point extraction and centroid positioning experiments are carried out. The results of the simulation experiments are shown in Table 1.

[0107] Table 1 Results of star point extraction and centroid positioning simulation experiments (pixels)

[0108]

[0109]

[0110] It can be seen from the results of the simulation experiments that under strong noise interference, the method of this patent successfully extracts all the star points in the field of view and has good positioning accuracy. The row coordinate error and column coordinate error of the star points are as Figure 5 、 Figure 6 shown.

[0111] The above simulation analysis is only based on one star map under the condition that the standard deviation is 6. In order to further investigate the star point extraction success rate of the method and verify the above analysis, first, 1000 different star maps are simulated by setting different optical axis pointing parameters, and Gaussian white noise with different standard deviations is added respectively to test the overall performance level of the method in different working environments. When given Gaussian white noise with different standard deviations, the star point extraction success rate of the method is shown in Table 2 below.

[0112] Table 2 Star point extraction success rate of the method under different noise standard deviations

[0113]

Claims

1. A star point extraction method based on attitude information, characterized in that: Randomly select a sampling window according to the actually captured star map, calculate the expectation, standard deviation and threshold of the gray values of all pixels within each sampling window; determine the size of the ordinate matrix according to the noise intensity of the star map, and screen out the ordinates and potential pixel points of potential pixels; perform first-order forward difference on each row of the ordinate matrix to obtain a difference matrix; If the ordinate matrix is a seed point, then perform first-order forward difference on a certain row of pixel points in the internal area of the same star point to obtain a constant sequence; Traverse each row of the difference matrix, extract seed points by judging the values of each row of the difference matrix, and eliminate similar seed points based on the Manhattan distance; according to the coordinate information of the seed points, use the region growing method to search for all internal pixels of the star point and perform centroid positioning; according to the attitude change amount of the inertial device, output the seed points of the star points in the subsequent captured star maps recursively, and perform region growing and centroid positioning operations, including five steps: constructing the ordinate matrix M, constructing the difference matrix Q, eliminating noise points and extracting seed points, accurately extracting internal pixels of the star point and centroid positioning, and recursively outputting the centroid position of the star point based on the attitude change amount of the inertial device. Specifically: Step 1: Traverse the star map S once to obtain a two-dimensional ordinate matrix M; the specific steps are as follows: Step 1.1: Determine the threshold T by the following method: Randomly select dozens of sampling windows with uniform distribution and appropriate size that can reflect the noise characteristics, and calculate the expectation of all pixel gray values within each sampling window. and the standard deviation , and then calculate the threshold T according to the following formula for star map noise reduction processing; （1） Wherein, is the expectation of the gray values of all pixels within the sampling window, is the standard deviation of the gray values of all pixels within the sampling window, is the number of sampling windows, is an empirical value, depending on the test results; Step 1.2: For a captured star map S, assume the size of the star map is N1*N2; where N1 is the number of rows of the star map and N2 is the number of columns of the star map; construct a vertical coordinate matrix M, where the size of M is (N1 / 2)*N3. The reason it is called the vertical coordinate matrix is that the non-zero values stored in the matrix are the vertical coordinates of potential pixel points; the number of rows of the M matrix is half the number of rows of the S matrix, and N3 is a constant value determined according to the noise intensity of the star map. The greater the noise intensity, the more noise pixel points with high gray values (i.e., noise points) there are in the image, and the more potential pixel points will appear when searching for seed points later, so N3 is larger. Any pixel point in the internal area of a star point is called a seed point of the star point; each row of the vertical coordinate matrix M stores the vertical coordinates of the potential pixels selected from the corresponding row of the star map; the selected potential pixel points are the set of strong noise points with gray values greater than the threshold and the seed points of different star points. Subsequently, the vertical coordinate matrix M will be processed twice to remove the noise points therein and retain the seed points; after obtaining these seed points, all the internal pixel points of different star points can be further quickly searched for centroid positioning; Step 1.3: Construct the ordinate matrix M as follows: First, traverse each pixel point in the first row of the star map from left to right. When encountering the first pixel point with a gray value greater than the threshold T, store the ordinate of the pixel point in the M(1, 1) position of the M matrix. When encountering the second pixel point with a gray value greater than the threshold T, store the ordinate of the pixel point in the M(1, 2) position of the M matrix, and so on, until scanning the first row data of the star map; then, traverse each pixel point in the third row of the star map from left to right. When encountering the first pixel point with a gray value greater than the threshold T, store the ordinate of the pixel point in the M(2, 1) position of the M matrix, and so on, until scanning the third row data of the star map; according to this mode, scan the entire star map with a row step size of 2 to obtain the ordinate matrix M; Step 2: Perform first-order forward difference on each row of the ordinate matrix M to obtain a difference matrix Q; Step 3: Eliminate noise points and extract seed points; Step 4: Based on the coordinate information of the seed points, use the region growing method to search for all internal pixels of the star point and perform centroid positioning; Step 5: Use the attitude change amount of the inertial device to recursively output the centroid position of the star points in the subsequent captured star maps.

2. The star point extraction method based on attitude information according to claim 1, characterized in that: The specific steps of "performing first-order forward difference on each row of the ordinate matrix M to obtain a difference matrix Q" in Step 2 are as follows: Step 2.1: Construct the difference matrix Q. The specific execution process is: Subtract the data M(i, j - 1) in the (j - 1)-th column of the i-th row of the ordinate matrix M from the data M(i, j) in the j-th column of the i-th row of the ordinate matrix M to obtain the data Q(i, j) in the j-th column of the i-th row of the difference matrix Q, that is （2） Step 2.2: Explain the mathematical meaning reflected by the first-order difference operation in removing noise points and extracting seed points in the subsequent steps; If the position (2i - 1, M(i, j)) of the star map S pointed to by a certain value M(i, j) in the ordinate matrix M is a seed point, that is, the pixel is in the inner region of the star point, then the pixel points (2i - 1, M(i, j) - 1) and (2i - 1, M(i, j) + 1) of the star map S are also in the inner region of the star point, or (2i - 1, M(i, j) - 2), (2i - 1, M(i, j) - 1), (2i - 1, M(i, j)), or (2i - 1, M(i, j)), (2i - 1, M(i, j) + 1), (2i - 1, M(i, j) + 2). Generally speaking, there are three adjacent pixel points in the inner region of the star point; if it is the pixel points (2i - 1, M(2i - 1, j) - 1), (2i - 1, M(i, j)), (2i - 1, M(i, j) + 1), for the ordinate matrix M, these three adjacent pixel points in the inner region of the star map will be recognized and their ordinates will be stored in step 1. Then there are three adjacent numbers (M(i, j) - 1, M(i, j), M(i, j) + 1) at a certain position in the i-th row of the matrix M; then, for a certain row of pixel points in the inner region of the same star point, the corresponding positions in the ordinate matrix M increase linearly, which is equivalent to the constant slope in a continuous function. At this time, the result obtained by performing the first-order forward difference on it is a constant sequence {1}; If a non-zero value M(i, j) in the ordinate matrix M points to a position (2i - 1, M(i, j)) in the star map S that is not a seed point, that is, a noise point, then the pixel points (2i - 1, M(i, j) - 1) and (2i - 1, M(i, j) + 1) of the star map S are not in the inner region of the star point, that is, the pixel points (2i - 1, M(i, j) - 1) and (2i - 1, M(i, j) + 1) of the star map S are considered to be noise points with lower gray values in step 1, and their ordinates will not be stored in the matrix M. Therefore, regardless of whether the values of M(i, j - 1) and M(i, j + 1) in the ordinate matrix M store the ordinates of strong noise points or seed points, M(i, j - 1), M(i, j), and M(i, j + 1) increase non-linearly, that is, M(i, j) - M(i, j - 1) ≠ 1 and M(i, j + 1) - M(i, j) ≠ 1.

3. A star point extraction method based on attitude information according to claim 1, characterized in that: The specific steps of "removing noise points and extracting seed points" described in step 3 are as follows: Step 3.1: Extract the set of seed points; traverse each row of the difference matrix Q, and extract the seed points by judging whether there are 2 or more consecutive 1 values in each row of the difference matrix Q, that is, if it satisfies: （3） Then: （4） In the formula, is the set of internal pixel points of a certain star point; are the horizontal and vertical coordinates of the seed point; Step 3.2: Eliminate the similar seed points in the seed point set; thus, the seed point set of all star points in the star map is obtained ; As can be seen from Step 1, the row step size during the traversal of the star map is 2. Although the row step size is 2, redundant seed points will still be generated, that is, some seed points in the seed point set belong to the same star point and need to be eliminated; for this purpose, the similar seed points are eliminated based on the Manhattan distance. If for the seed points , , when the Manhattan distance between the two is less than or equal to 5, it is considered that these two seed points are similar seed points, and any one of them can be eliminated at will, as follows: （5） In the formula, are two seed points , is the Manhattan distance.

4. A star point extraction method based on attitude information according to claim 1, characterized in that: The specific steps of "searching for all internal pixels of the star points using the region growing method based on the coordinate information of the seed points and performing centroid localization" described in step 4 are as follows: Step 4.1: Using the seed point as the initial growth point, the growth criterion for region growing is that the absolute value of the difference in gray values between the growth point and the adjacent pixels in its 8-neighborhood is less than a certain parameter k, where k ranges from 10 to 30. The core step of region growing is to start from the initial growth point, merge the pixels in the 8-neighborhood of the growth point that have similar features to it, regard the newly merged pixels as new growth points, and then execute the same steps as above based on these new growth points until there are no new growth points. Therefore, a suitable initial growth point and growth criterion are the key. The initial growth point has been obtained through steps 1, 2, and 3, and the growth criterion is as described above. Finally, all internal pixel points of each star point are obtained; Step 4.2: With all the internal pixel points of the star point, the centroid coordinates of the star point are obtained according to the centroid localization formula as follows: （6） Wherein, is the abscissa of the centroid of the star point, is the ordinate of the centroid of the star point, is the abscissa of the th pixel point inside the star point, is the ordinate of the th pixel point inside the star point, is the gray value of the th pixel point inside the star point.

5. A star point extraction method based on attitude information according to claim 1, characterized in that: The specific steps of "using the attitude change amount of the inertial device to recursively output the centroid position of the star points in the subsequent captured star map" described in step 5 are as follows: Step 5.1: Determine the three-dimensional coordinates of the star vector in the star sensor system at the current moment ; After obtaining the centroid coordinates of the star vector on the CCD plane at the current moment through the above steps, for the subsequent star map shooting, the attitude change amount output of the inertial device is used to quickly obtain the star point seed points, and region growing and centroid positioning operations are performed, greatly improving the real-time level of the star sensor. The specific process is as follows; Obtain the three-dimensional coordinates of the stellar vector in the star sensor system at the current moment, as follows: , as follows: （7） In the formula, and are the horizontal and vertical coordinates of the centroid of the star point at a certain moment, and are the coordinates of the principal point of the star sensor, is the focal length of the star sensor; Step 5.2: Deduce the recurrence model between the centroid coordinates on the CCD plane of the same star at moment and moment; The three-dimensional coordinates of the star vector in the star sensor system at moment are , and The relationship is as follows: （8） In the formula, is the coordinate transformation matrix from the star sensor coordinate system at time t + Δt to the star sensor coordinate system at time t; Coordinate transformation matrix Obtained from the output of the attitude change amount of the inertial device as follows: （9） In the formula, is the angular velocity vector at time t, , is the skew-symmetric matrix of the vector , , , , are the angular increments of the three axes of the gyroscope and are known quantities, that is, the coordinate transformation matrix is known; Based on Equation (8) and Equation (9), it is derived that and The recurrence relation between them is as follows: （10） wherein, , are the horizontal and vertical coordinates of the centroid of the star point at a moment; Is very small and can be ignored, simplifying the above formula to: （11） So far, the predicted value of the centroid coordinates of the star point is output using the attitude change amount of the inertial device through equation (10), and then the predicted value is used as the seed point for region growing and centroid localization.

Images